Such a method and a corresponding device are disclosed in German patent application DE 10 2004 031 624 A1. In particular, this method and this device make it possible to control or regulate the level of reagent in the catalytic converter at a prescribed target storage value. On the one hand, the targeted specification of the target storage value ensures that, during non-stationary states of the internal combustion engine, a sufficient amount of reagent is available to eliminate at least one undesired exhaust gas component as completely as possible, and, on the other hand, that reagent leakage is avoided.